Method for automatic pressure control during drilling including correction for drill string movement

ABSTRACT

A method for determining annulus/wellbore fluid pressure, which is corrected for movement of a pipe string into or out of a wellbore, includes determining an initial annulus fluid pressure in the wellbore. Determining the initial annulus fluid pressure may include measuring a fluid flow rate into the wellbore and/or measuring a fluid pressure in the annulus proximate the surface. A rate of movement of a pipe string into or out of the wellbore is also determined. The initial annulus fluid pressure is adjusted to a corrected annulus fluid pressure by an amount which is a function of the rate of motion of the pipe string, a surface area of the outer wall of the pipe string and a surface area of the inner wall of the wellbore.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No. 61/450,646, filed on Mar. 9, 2011, which is incorporated herein by reference.

BACKGROUND

The exploration for and production of hydrocarbons from subsurface rock formations requires devices to reach and extract the hydrocarbons from the rock formations. Such devices are typically wellbores drilled from the Earth's surface to the hydrocarbon-bearing rock formations in the subsurface. The wellbores are drilled using a drilling rig. In its simplest form, a drilling rig is a device used to support a drill bit mounted on the end of a pipe known as a “drill string.” A drill string is typically formed from lengths of drill pipe or similar tubular segments threadedly connected end to end. The drill string is longitudinally supported by the drilling rig structure at the surface, and may be rotated by devices associated with the drilling rig such as a top drive, or kelly/kelly busing assembly. A drilling fluid made up of a base fluid, typically water or oil, and various additives is pumped down a central opening in the drill string. The fluid exits the drill string through openings called “jets” in the body of the rotating drill bit. The drilling fluid then circulates back toward the surface in an annular space formed between the wellbore wall and the drill string, carrying the cuttings from the drill bit so as to clean the wellbore. The drilling fluid is also formulated such that the fluid pressure applied by the drilling fluid is typically greater than the surrounding formation fluid pressure, thereby preventing formation fluids from entering the wellbore and the collapse of the wellbore. However, such formulation also must provide that the hydrostatic pressure does not exceed the pressure at which the formations exposed by the wellbore will fail (fracture).

It is known in the art that the actual pressure exerted by the drilling fluid (“hydrodynamic pressure”) is related to its formulation as explained above, its other rheological properties, such as viscosity, and the rate at which the drilling fluid is moved through the drill string into the wellbore. It is also known in the art that, by suitable control over the discharge of drilling fluid from the wellbore through the annular space, it is possible to exert pressure in the annular space between the drill string and the wellbore wall that exceeds the hydrostatic and hydrodynamic pressures by a selected amount. There have been developed a number of drilling systems called “dynamic annular pressure control” (DAPC) systems that perform the foregoing fluid discharge control. One such system is disclosed, for example, in U.S. Pat. No. 6,904,981 issued to van Riet and assigned to the assignee of the present disclosure. The DAPC system disclosed in the '981 patent includes a fluid backpressure system in which fluid discharge from the borehole is selectively controlled to maintain a selected pressure at the bottom of the borehole, and fluid may be pumped down the drilling fluid return system to maintain annulus pressure during times when the mud pumps are turned off (and no mud is pumped through the drill string). A pressure monitoring system is further provided to monitor detected borehole pressures, model expected borehole pressures for further drilling and to control the fluid backpressure system. U.S. Pat. No. 7,395,878 issued to Reitsma et al. and assigned to the assignee of the present disclosure describes a different form of DAPC system.

The formulation of the drilling fluid, and when used, supplemental control over the fluid discharge such as by using a DAPC system, are intended to provide a selected fluid pressure in the wellbore during drilling. Such fluid pressure is, as explained above, selected so that fluid from the pore spaces of certain subsurface formations does not enter the wellbore, so that the wellbore remains mechanically stable during continued drilling operations, and so that exposed rock formations are not hydraulically fractured or distended during drilling operations. DAPC systems, in particular, provide increased ability to control the fluid pressure in the wellbore during drilling operations without the need to reformulate the drilling fluid extensively. As explained in the patents referenced above, using DAPC systems may also enable drilling wellbores through formations having fluid pressures and fracture pressures such that drilling using only formulated drilling fluid and uncontrolled fluid discharge from the wellbore is essentially impossible.

Movement of the drill string axially along the wellbore creates changes in the wellbore annulus fluid pressure as a result of fluid friction effects between the outside surface of the pipe string and the wall of the wellbore. The amount of change in annulus fluid pressure is related to the exterior geometry of the drill string, the geometry of the wellbore wall, the rheological properties of the drilling fluid and the speed at which the drill string is moved into the wellbore (sometimes called “surge” pressure; i.e., an increase in pressure, depending on the drill string movement rate) or is removed from the wellbore (sometimes called “swab” pressure, i.e., a reduction in pressure, depending on the drill string movement rate). Various techniques are known in the art for direct calculation of surge and swab pressures; however, the known techniques require implementation of complex algorithms related to the geometry of the drill string and the wellbore. Other techniques may determine the wellbore annulus pressure proximate the bottom of the well.

There is a need for techniques to estimate, preferably in real time, the changes in dynamic wellbore fluid pressure affected by axial drill string movement in order to better select drilling operating parameters for efficient drilling operations.

SUMMARY

A method according to the disclosure for determining wellbore fluid pressure, corrected for drill string movement effects during wellbore drilling operations, includes the step of determining an initial annulus fluid pressure in the wellbore. Determining the initial annulus/wellbore fluid pressure may be accomplished in any manner known to those of skill in the art and may include the steps of measuring a fluid flow rate into the wellbore and/or measuring a fluid pressure in the annulus proximate the surface. A rate of movement of a pipe string into or out of the wellbore is also determined. The determined initial annulus fluid pressure is then adjusted to a corrected annulus fluid pressure by an amount that is a function of the rate of movement of the pipe string, a surface area of the outer wall of the pipe string and a surface area of the inner wall of the wellbore In one or more embodiments, the annulus fluid pressure is determined and adjusted in real time.

Other aspects and advantages of one or more embodiments of the invention will be apparent from the following description and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example of a wellbore drilling unit including a dynamic annular pressure control (DAPC) system.

FIGS. 2A and 2B show an example of calculating surge pressure according to an embodiment of the disclosure.

FIGS. 3A and 3B shown an example of calculating swab pressure according to an embodiment of the disclosure.

FIG. 4 shows a comparison of using the method according to an embodiment of the disclosure for calculating an increase in wellbore fluid pressure resulting from drill string movement into the wellbore with prior art methods for calculating such an increase in wellbore fluid pressure.

FIG. 5 shows a comparison of using the method according to an embodiment of the disclosure for calculating a decrease in wellbore fluid pressure resulting from drill string movement out of the wellbore with prior art methods for calculating such a decrease in wellbore fluid pressure.

DETAILED DESCRIPTION

Methods according to one or more embodiments of the disclosure in general make use of a dynamic annular pressure control (DAPC) system during drilling operations involving a wellbore to adjust the fluid pressure in a wellbore annulus (i.e., the annular space between the wall of the wellbore and the exterior of the drill string) to selected values that are adjusted or corrected to account for movement of the drill string into or out of the wellbore.

An example of a drilling unit drilling a wellbore through subsurface rock formations, including a dynamic annular pressure control (DAPC) system is shown schematically in FIG. 1. Operation and details of the DAPC system may be substantially as described in U.S. Pat. No. 7,395,878 issued to Reitsma et al. and assigned to the assignee of the present disclosure or may be as described in U.S. Pat. No. 6,904,981 issued to van Riet and assigned to the assignee of the present disclosure, both incorporated herein by reference.

The drilling system 100 includes a hoisting device known as a drilling rig 102 that is used to support drilling operations through subsurface rock formations, such as shown at 104. Many of the components used on the drilling rig 102, such as a kelly (or top drive), power tongs, slips, draw works and other equipment are not shown for clarity of the illustration. A wellbore 106 is shown being drilled through the rock formations 104. A drill string 112 is suspended from the drilling rig 102 and extends into the wellbore 106, thereby forming an annular space (annulus) 115 between the wellbore wall and the drill string 112, and/or between a casing 101 (when included in the wellbore) and the drill string 112. One of the functions of the drill string 112 is to convey a drilling fluid 150 (shown in a storage tank or pit 136), the use of which is for purposes as explained in the Background section herein, to the bottom of the wellbore 106 and into the wellbore annulus 115.

The drill string 112 supports a bottom hole assembly (“BHA”) 113 proximate the lower end thereof that includes a drill bit 120, and may include a mud motor 118, a sensor package 119, a check valve (not shown) to prevent backflow of drilling fluid from the annulus 115 into the drill string 112. The sensor package 119 may be, for example, a measurement while drilling and logging while drilling (MWD/LWD) sensor system. In particular the BHA 113 may include a pressure transducer 116 to measure the pressure of the drilling fluid in the annulus 115 near the bottom of the wellbore 106. The BHA 113 shown in FIG. 1 can also include a telemetry transmitter 122 that can be used to transmit pressure measurements made by the transducer 116, MWD/LWD measurements as well as drilling information to be received at the surface. A data memory including a pressure data memory may be provided at a convenient place in the BHA 113 for temporary storage of measured pressure and other data (e.g., MWD/LWD data) before transmission of the data using the telemetry transmitter 122. The telemetry transmitter 122 may be, for example, a controllable valve that modulates flow of the drilling fluid through the drill string 112 to create pressure variations detectable at the surface. The pressure variations may be coded to represent signals from the MWD/LWD system and the pressure transducer 116.

The drilling fluid 150 may be stored in a reservoir 136, which is shown in the form of a mud tank or pit. The reservoir 136 is in fluid communications with the intake of one or more mud pumps 138 that in operation pump the drilling fluid 150 through a conduit 140. An optional flow meter 152 can be provided in series with one or more mud pumps 138, either upstream or downstream thereof. The conduit 140 is connected to suitable pressure sealed swivels (not shown) coupled to the uppermost segment (“joint”) of the drill string 112. During operation, the drilling fluid 150 is lifted from the reservoir 136 by the pumps 138, is pumped through the drill string 112 and the BHA 113 and exits the through nozzles or courses (not shown) in the drill bit 120, where it circulates the cuttings away from the bit 120 and returns them to the surface through the annulus 115. The drilling fluid 150 returns to the surface and goes through a drilling fluid discharge conduit 124 and optionally through various surge tanks and telemetry systems (not shown) to be returned, ultimately, to the reservoir 136.

A pressure isolating seal for the annulus 115 is provided in the form of a rotating control head forming part of a blowout preventer (“BOP”) 142. The drill string 112 passes through the BOP 142 and its associated rotating control head. When actuated, the rotating control head on the BOP 142 seals around the drill string 112, isolating the fluid pressure therebelow, but still enables drill string rotation and longitudinal movement. Alternatively, a rotating BOP (not shown) may be used for essentially the same purpose. The pressure isolating seal forms a part of a back pressure system (a greater portion of which is represented by dotted box 131) used to maintain a selected fluid pressure in the annulus 115.

As the drilling fluid returns to the surface it goes through a side outlet below the pressure isolating seal (rotating control head) to a back pressure system 131 configured to provide an adjustable back pressure on the drilling fluid in the annulus 115. The back pressure system may comprise a variable flow restrictive device, suitably in the form of a wear resistant choke 130, which applies a corresponding back pressure on the drilling fluid in the annulus 115 as flow is restricted through such device. It will be appreciated that chokes exist that are designed to operate in an environment where the drilling fluid 150 contains substantial drill cuttings and other solids. The choke 130 is one such type and is further capable of operating at variable pressures, flowrates and through multiple duty cycles.

The drilling fluid 150 exits the choke 130 and flows through an optional flow meter 126 to be directed through an optional degasser 1 and solids separation equipment 129. The degasser 1 and solids separation equipment 129 are designed to remove excess gas and other contaminants, including drill cuttings, from the drilling fluid 150. After passing through the solids separation equipment 129, the drilling fluid 150 is returned to reservoir 136.

The flow meter 126 may be a mass-balance type or other high-resolution flow meter. A pressure sensor 147 can be optionally provided in the drilling fluid discharge conduit 124 upstream of the variable flow restrictive device (e.g., the choke 130). A flow meter, similar to flow meter 126, may be placed upstream of the back pressure system 131 in addition to the back pressure sensor 147. A back pressure control means, e.g. preferably a programmed computer system but which may also be a trained operator, monitor data relevant for the annulus pressure, including data from a pressure monitoring system 146 (i.e., pressure sensor data), and provide control signals to at least the back pressure system 131 (and/or specifically to the back pressure pump 128) and optionally also to the injection fluid injection system.

In general terms, the required back pressure to obtain the desired annulus pressure proximate the bottom of the wellbore 106 can be determined by obtaining, at selected times, information on the existing pressure of the drilling fluid in the annulus 115 in the vicinity of the BHA 113, referred to as the bottom hole pressure (BHP), comparing the information with a desired BHP and using the differential between these for determining a set-point back pressure. The set point back pressure is used for controlling the back pressure system in order to establish a back pressure close to the set-point back pressure. Information concerning the fluid pressure in the annulus 115 proximate the BHA 113 may alternatively be determined using an hydraulic model and measurements of drilling fluid pressure as it is pumped into the drill string and the rate at which the drilling fluid is pumped into the drill string (e.g., using a flow meter or a “stroke counter” typically provided with piston type mud pumps). The BHP information thus obtained may be periodically checked and/or calibrated using measurements made by the pressure transducer 116.

The injection fluid pressure in an injection fluid supply 143 passage represents a relatively accurate indicator for the drilling fluid pressure in the drilling fluid gap at the depth where the injection fluid is injected into the drilling fluid gap. Therefore, a pressure signal generated by an injection fluid pressure sensor anywhere in the injection fluid supply passage, e.g., at 156, can be suitably used to provide an input signal for controlling the back pressure system 131 (e.g., choke 130), and for monitoring the drilling fluid pressure in the wellbore annulus 115.

The pressure signal can, if so desired, optionally be compensated for the density of the injection fluid column and/or for the dynamic pressure loss that may be generated in the injection fluid between the injection fluid pressure sensor 156 in the injection fluid supply passage and where the injection into the drilling fluid return passage takes place 144, for instance, in order to obtain an exact value of the injection pressure in the drilling fluid return passage at the depth 144 where the injection fluid is injected into the drilling fluid gap.

The pressure of the injection fluid in the injection fluid supply passage 141 is advantageously utilized for obtaining information relevant for determining the current bottom hole pressure. As long as the injection fluid is being injected into the drilling fluid return stream, the pressure of the injection fluid at the injection depth can be assumed to be equal to the drilling fluid pressure at the injection point 144. Thus, the pressure as determined by the injection fluid pressure sensor 156 can advantageously be used to generate a pressure signal for use as a feedback signal for controlling or regulating the back pressure system 131.

It should be noted that the change in hydrostatic contribution to the down hole pressure that would result from a possible variation in the injection fluid injection rate, is in close approximation compensated by the above-described controlled re-adjusting of the back pressure system 131 by the back pressure control means. Thus, by controlling the back pressure system 131, the fluid pressure in the bore hole 106 is almost independent of the rate of injection fluid injection.

One possible way to use the pressure signal corresponding to the injection fluid pressure, is to control the back pressure system 131 so as to maintain the injection fluid pressure on a certain suitable constant value throughout the drilling or completion operation. The accuracy is increased when the injection point 144 is in close proximity to the bottom of the bore hole 106.

When the injection point 144 is not so close to the bottom of the wellbore 106, the magnitude of the pressure differential over the part of the drilling fluid return passage stretching between the injection point 144 and the bottom of the wellbore 106 is preferably established. For this situation, a hydraulic model can be utilized as will be described below.

In one example, the pressure difference of the drilling fluid in the drilling fluid return passage in a lower part of the wellbore 106 extending between the injection fluid injection point 144 and the bottom of the well bore 106, can be calculated using a hydraulic model taking into account inter alia the well geometry. Because the hydraulic model is generally only used for calculating the pressure differential over a relatively small section of the wellbore 106, the precision is expected to be much better than when the pressure differential over the entire wellbore length must be calculated.

In this example, the back pressure system 131 can be provided with a back pressure pump 128, in fluid communication with the wellbore annulus 115 and the choke 130, to pressurize the drilling fluid in the drilling fluid discharge conduit 124 upstream of the flow restrictive device 130. The intake of the back pressure pump 128 is connected, via conduit 119A/B, to a drilling fluid supply which may be the reservoir 136. A stop valve 125 may be provided in conduit 119A/B to isolate the back pressure pump 128 from the drilling fluid supply 136. Optionally, a valve 123 may be provided to selectively isolate the back pressure pump 128 from the drilling fluid discharge conduit 124 and choke 130.

The back pressure pump 128 can be engaged to ensure that sufficient flow passes the choke 130 to be able to maintain backpressure, even when there is insufficient flow coming from the wellbore annulus 115 to maintain pressure on the choke 130. However, in some drilling operations it may often suffice to increase the weight of the fluid contained in the upper part 149 of the well bore annulus by reducing the injection fluid injection rate when the circulation rate of drilling fluid 150 via the drill string 112 is reduced or interrupted.

The back pressure control means in the present example can generate the control signals for the back pressure system 131, suitably adjusting not only the variable choke 130 but also the back pressure pump 128 and/or valve 123.

In this example, the drilling fluid reservoir 136 also comprises a trip tank 2 in addition to the illustrated mud tank or pit. A trip tank is normally used on a drilling rig to monitor drilling fluid gains and losses during movement of the drill string into and out of the wellbore 106 (known as “tripping operations”). The trip tank 2 may not be used extensively when drilling using a multiphase fluid system involving injection of a gas into the drilling fluid return stream, because the wellbore 106 may often remain alive (i.e., continuously flowing) or the drilling fluid level in the well bore 106 drops when the injection gas pressure is bled off. However, in the present embodiment, the functionality of the trip tank 2 is maintained, for instance, for those occasions when a high-density drilling fluid is pumped down into high-pressure wells.

A valve manifold system 5, 125 can be provided downstream of the back pressure system 131 to enable selection of the reservoir to which drilling mud returning from the wellbore 106 is directed. In the present example, the valve manifold system 5, 125 can include a two way valve 5, allowing drilling fluid 150 returning from the well bore 106 to be directed to the mud pit 136 or the trip tank 2.

The valve manifold system 5, 125 may also include a two way valve 125 provided for either feeding drilling fluid 150 from reservoir 136 via conduit 119A or from trip tank/reservoir 2 via conduit 119B to backpressure pump 128, optionally provided in fluid communication with the drilling fluid return passage 115 and the choke 130.

In operation, valve 125 is operated to select either conduit 119A or conduit 119B and the backpressure pump 128 is engaged to ensure sufficient flow passes the choke 130 so that backpressure on the annulus 115 is maintained, even when there is little to no flow coming from the annulus 115. Unlike the drilling fluid passage inside the drill string 112, the injection fluid supply 143 passage can preferably be dedicated to one task, which is supplying the injection fluid for injection into the drilling fluid gap, e.g., at injection point 144. In this way, the hydrostatic and hydrodynamic interaction of the drilling fluid with the injection fluid can be accurately determined and kept constant during a drilling operation, so that the weight of the injection fluid and dynamic pressure loss in the supply passage 141 can be accurately established.

The description of the drilling system above with reference to FIG. 1 is to provide an example of drilling a wellbore using a DAPC system which can determine and maintain annulus/wellbore fluid pressure near the bottom of the wellbore 106, i.e., the above-described BHP, near a selected/desired value. Such DAPC system may include a hydraulics model that, as explained above, uses as input the rheological properties of the drilling mud/fluid 150, the rate at which the mud/fluid flows into the wellbore 106, the wellbore and drill string configuration, pressure on the discharge conduit 124 and if available, measurements of annulus fluid pressure proximate the bottom of the wellbore (e.g., from transducer 116) or proximate the surface to supplement or refine calculations made by the hydraulics model, e.g., to determine an initial wellbore fluid pressure.

In one or more methods according to one or more embodiments of the invention, the DAPC system may be operated in a specific manner to adjust the BHP for pressure changes, i.e., increases and/or decreases, resulting from drill string movement, e.g., by adding or subtracting the pressure increase or pressure decrease, respectively. An increase in BHP may be created by fluid friction in the fluid disposed in the annular space 115 in the wellbore 106 when the drill string 112 is moved into the wellbore 106. The magnitude of the pressure increase is related to the surface area of the annular space 115 (per unit length), the length of the drill string 115 in the wellbore 106, the frictional and viscous properties of the fluid, and the speed/rate at which the drill string 112 is moved into the wellbore 106. Conversely, a decrease in BHP may be created by fluid friction in the fluid disposed in the annular space 115 in the wellbore 106 when the drill string 112 is moved out of the wellbore 106. The magnitude of the pressure decrease is related to the foregoing factors as well as the rate at which the drill string 112 is removed from the wellbore 106. The rate of movement of a pipe string into or out of the wellbore is determined in any manner known to those skilled in the art.

Pressure increases (and/or decreases) resulting from drill string movement may be initially determined in real time by measuring the increased fluid flow out of (or into) the wellbore upon movement of the drill string. Such flow out of or into the wellbore may be conducted, e.g., via flow meter disposed proximate the discharge conduit 124. The pressure increases (and/or decreases) resulting from drill string movement may alternatively be initially determined in real time by converting the fluid displacement (or placement), as a result of the drill string movement into (or out of) the wellbore, into an analogous pressure increase (or decrease), e.g., as if the fluid were being pumped. However, such initial determinations of pressure increases (i.e., surge pressures) or decreases (i.e., swab pressures) do not account for all of the factors given above that may affect the actual pressure increases or decreases due to drill string/pipe string movement into and out of the wellbore.

Referring to FIG. 2B, an increase in annulus fluid pressure (i.e., a surge pressure or tripping in pressure) due to drilling string 112 movement into the wellbore 106 is generally understood to be related to (and/or a function of) the drilling fluid properties, the surface area of the drill string 112 and the wellbore 106 (per unit length) and the rate at which the drill string 112 is moved into the wellbore 106. FIG. 2B shows the drill string 112 being moved into the wellbore 106 through a casing 101, which may be disposed therein was disclosed with reference to FIG. 1. Fluid flow out of the annular space 115 in the wellbore 106 may be diverted through an outlet 124 by a rotating control head 142 or rotating blowout preventer, as previously disclosed.

Referring now to FIG. 2A, a cross sectional view through a portion of the drill string 112 disposed in the wellbore 106 (as designated by the hash marks on FIG. 2B) is illustrated, and presents the calculations that may be performed according to one or more embodiments of the invention to determine surge pressure. The rate at which the drill string 112 is moved into the wellbore 106 is a readily measured quantity. Such rate may be referred to as “tripping in” speed or may also include the rate of lengthening or rate of penetration of the formations during drilling (called “ROP”), and is represented by V_(dp) and the downward arrow in FIG. 2A. The respective surface areas of the drill string 112 and wellbore annular space 115 per unit length are functions of A₂ and A₁. Drilling fluid velocity, as a result of pumping or as represented by pumping, at a position proximate the wellbore wall is represented by V_(f) and the upward arrow in FIG. 2A. Fluid velocity relative to (i.e., proximate) the moving drill string 112 may be represented by V_(r1) (and the accompanying directional arrow), and as will be recognized by those skilled in the art, is a relation between V_(f) and V_(dp) (rarely, but sometimes, being the sum of the these two quantities). A fluid pressure F_(Surge) as a result of moving the drill string 112 into the wellbore 106 is a function of V_(r1) as well as the surface areas A₂ and A₁ (per unit length) and may be represented by F_(Surge){V_(r1), (A₂, A₁)}. An exemplary equation for calculating F_(surge) is presented below:

F _(surge)=(μV _(r1) Lc ₁)/A _(p)

wherein, μ is the fluid viscosity, V_(r1) is the drill string velocity or fluid velocity relative to the drill string, L is the length of the pipe, c₁ is a constant and A_(p) represents the surface area of the annular space (per unit length). Those skilled in the art will readily recognize and appreciate that the constant is dependent on a number of fluid mechanic properties specific to the wellbore/drilling operation and that the surface area of the annular space (per unit length) is a readily calculated quantity as a function of A₂ and A₁.

A fluid pressure F_(DrillOp) due to the drilling operation as a result of movement of the fluid through the drill string 112, excepting movement of the drill string 112, is a function of V_(f) and the surface areas A₂ and A₁ (per unit length) and may be represented by F_(DrillOp) {V_(f), (A₂, A₁)}. An exemplary equation for calculating F_(DrillOp) is presented below:

F _(DrillOp)=(μV _(f) Lc ₁)/A _(c)

wherein, μ is the fluid viscosity, V_(f) is the fluid velocity, L is the length of the pipe, c₁ is a constant and A_(c) represents the surface area of the annular space (per unit length). Those skilled in the art will readily recognize and appreciate that the constant is dependent on a number of fluid mechanic properties specific to the wellbore/drilling operation and that the surface area of the annular space (per unit length) is a readily calculated quantity as a function of A₂ and A₁.

A ratio of the fluid pressure due to movement of the drill string 112 into the wellbore 106 with respect to the fluid pressure due to the drilling operation (i.e., fluid movement alone) may be used to calculate a “friction mechanism factor”, f, (i.e., an empirical correction factor) as represented by the following equation:

$\begin{matrix} {f = {{Pressure}_{{Tripping}\mspace{14mu} {In}}/{Pressure}_{{Drilling}\mspace{14mu} {Operations}}}} \\ {= {F_{Surge}{\left\{ {V_{r\; 1},\left( {A_{2},A_{1}} \right)} \right\}/F_{DrillOp}}\left\{ {V_{f},\left( {A_{2},A_{1}} \right)} \right\}}} \\ {= {\left( {V_{r\; 1}*A_{c}} \right)/\left( {V_{f}*A_{p}} \right)}} \end{matrix}$

As is readily apparent in the above equation, the friction mechanism factor, f, is not dependent upon the viscosity of the fluid or a constant, as are the fluid pressures F_(Surge) and F_(DrillOp).

While a value of the friction mechanism factor may be calculated via the above equations, the value off may also be calibrated and/or determined, for example, by using pressure measurements made in the annular space 115 proximate the bottom end portion of the drill string while drilling (“pressure while drilling” or PWD) or by observation of change in pressure in the annular space 115 measured proximate the surface at known rates of movement of the drill string 112 into the wellbore 106. The friction mechanism factor is preferably calculated in real time and used to correct the initially determined surge pressure in real time. Experimentation has shown that an friction mechanism factor value of about 1.2 to 1.3 adequately corrects such determined surge pressure for any selected drill string speed into the wellbore 106. The friction mechanism factor also corrects for other conditions in the wellbore 106, which may affect an accurate determination of surge pressure. Such conditions may include solids in the drilling fluid, temperature changes with depth and changes in the geometry of the well with depth.

Conversely, and now referring to FIGS. 3A and 3B, movement of the drill string 112 out of the wellbore 106 may result in a decrease in annular fluid pressure (i.e., a swab pressure or tripping out pressure). In FIG. 3A, a surface area of the interior of the drill string 112 per unit length may be represented by A₃, and is usually a consideration because the one-way check valve disposed at the bottom end portion of the drill string 112 permits fluid inside the drill string 112 to flow down and out of the drill string 112 when the drill string 112 is moved out of the wellbore 106. A fluid pressure F_(Swab) as a result of moving the drill string 112 out of the wellbore 106 is a function of V_(r1) and the surface areas A₃, A₂ and A₁ (per unit length) and may be represented by F_(Swab){V_(r1), (A₃, A₂, A₁)}. A fluid pressure F_(DrillOp) as a result of movement of the fluid through the drill string 112, excepting movement of the drill string 112 is a function of V_(f) and the surface areas A₂ and A₁ (per unit length) and may be represented byF {V_(f), (A₂, A₁)}, just as is done for determining a surge pressure. A ratio of the fluid pressure due to movement of the drill string 112 out of the wellbore 106 with respect to the fluid pressure due to drilling fluid movement alone may also be used to calculate a “friction mechanism factor”, f, (i.e., an empirical correction factor) as represented by the following equation:

$\begin{matrix} {f = {{Pressure}_{{Tripping}\mspace{14mu} {Out}}/{Pressure}_{{Drilling}\mspace{14mu} {Operations}}}} \\ {= {F_{Swab}{\left\{ {V_{r\; 1},\left( {A_{3},A_{2},A_{1}} \right)} \right\}/F_{DrillOp}}\left\{ {V_{f},\left( {A_{2},A_{1}} \right)} \right\}}} \\ {= {\left( {V_{r\; 1}*A_{c}} \right)/\left( {V_{f}*A_{p}} \right)}} \end{matrix}$

wherein, A_(p) in this instance represents the surface area of the annular space (per unit length) as a function of A₃, A₂ and A₁.

While a value of the friction mechanism factor may be calculated via the above equations, the value off may also be calibrated and/or determined, for example, by using pressure measurements made in the annular space 115 proximate the bottom end portion of the drill string while drilling (PWD) or by observation of change in pressure in the annular space 115 measured proximate the surface at known rates of movement of the drill string 112 out of the wellbore 106. The friction mechanism factor is preferably calculated in real time and used to correct the initially determined swab pressure in real time. Experimentation has shown that an friction mechanism factor value of about 1.2 to 1.3 adequately corrects such determined swab pressure for any selected drill string speed out of the wellbore 106. The friction mechanism factor also corrects for other conditions in the wellbore 106, which may affect an accurate determination of surge pressure. Such conditions may include solids in the drilling fluid, temperature changes with depth and changes in the geometry of the well with depth.

FIG. 4 graphically shows comparisons of surge pressures calculated using the method according to one or more embodiments of the invention with surge pressures calculated using several selected techniques known in the art. The calculated/estimated surge pressures are graphed versus running speed of the drill/pipe string. The increase in annulus pressure (i.e., surge pressure) with respect to drill string movement speed using a method known as the Shell IDM method is shown at curve 20. A technique explained in the reference by N.J. Lapeyrouse, Formulas and Calculations for Drilling, Production and Workover (Elsevier 2002), has its calculated increases in annulus pressure shown by curve 30. Curve 26 shows results obtained using a surge and swab calculation technique developed by Texas A&M University, College Station, Texas USA. Curve 28 shows increases in annulus fluid pressure calculated using the American Petroleum Institute (API) recommended practice 13D. The results obtained using the method according to one or more embodiments of the invention is shown at curve 24. The measured surge pressures using pressure measurement on the drill string (PWD) are shown at curve 22. As illustrated in FIG. 4, such measured surge pressures at curve 22 confirm the greater accuracy at curve 24 of using the method of one or more embodiments of the invention.

FIG. 5 graphically shows comparative results of using the various methods of FIG. 4 for determining swab pressures (resulting from movement of the drill string out of the wellbore). The calculated/estimated swab pressures are graphed versus running speed of the drill/pipe string. The results shown by curves 20A through 30A correspond to the results shown in FIG. 4 for the techniques/methods referenced by curves 20 through 30, respectively.

In specific examples of the method according to one or more embodiments of the invention, so called “surge” and “swab” pressures may be calculated. Surge pressure is generally known as the change in annulus fluid pressure resulting from movement of the drill string into the wellbore at relatively high speeds during “tripping in” operations, i.e., where the drill string is partially or totally reassembled to move the lower end thereof to the bottom of the wellbore or other position in the wellbore. Swab pressure, conversely, is generally known as the change in annulus fluid pressure when the drill string is partially or totally disassembled and is correspondingly removed from the wellbore at relatively high speeds. It is to be clearly understood, however, that the present method is applicable to drill string movement at any speed into or out of the wellbore, and is therefore not limited to calculation of surge and/or swab pressures.

The foregoing examples of the present method are described in terms of a drill string being moved into and out of a wellbore. It is also to be understood that the invention is not limited to use with a “drill string” as that term is ordinarily understood (i.e., having drilling instruments proximate the bottom thereof). For purposes of this disclosure, any type of pipe whose external dimensions are determinable may be used with one or more methods disclosed herein. Such pipe may be referred to generally as a “pipe string.”

One or more methods according to the invention provide an accurate calculation of change in annulus fluid pressure at any pipe speed into or out of a wellbore. Furthermore, the calculated increase or decrease in fluid pressures may be used in connection with the DAPC system, as explained with reference to FIG. 1, to maintain a selected fluid pressure in the annular space (i.e., maintain the fluid pressure in the annular space near a selected value), notwithstanding pressure changes caused by pipe movement effects.

While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as disclosed herein. Accordingly, the scope of the invention should be limited only by the attached claims. 

1. A method for determining wellbore fluid pressure, corrected for movement of a pipe string within a wellbore, the method comprising the steps of: determining a rate of movement of a pipe string within a wellbore; determining an initial wellbore fluid pressure at a position within an annular space of the wellbore, the annular space being defined between an outer wall of the pipe string and an inner wall of the wellbore; and adjusting the initial wellbore fluid pressure to a corrected wellbore fluid pressure by an amount that is at least a function of the rate of movement of the pipe string, a surface area of the outer wall of the pipe string and a surface area of the inner wall of the wellbore.
 2. The method of claim 1 wherein the step of adjusting the initial wellbore fluid pressure includes the step of: determining a pressure change in the annular space of the wellbore resulting from movement of the pipe string.
 3. The method of claim 2 wherein the step of determining a pressure change in the annular space of the wellbore resulting from movement of the pipe string is calculated using a flow rate of fluid flowing from the wellbore, the flow rate measured with a flow meter disposed in a fluid discharge conduit in fluid communication with the annular space of the wellbore.
 4. The method of claim 2 wherein the step of determining a pressure change in the annular space of the wellbore resulting from movement of the pipe string is a function of fluid displacement of the pipe string in the wellbore, the fluid displacement calculated using volumetric dimensions of the pipe string within the wellbore.
 5. The method of claim 2 wherein an empirical correction factor is used to correct the determined pressure change, the empirical correction factor being a function of the rate of movement of the pipe string, the surface area of the outer wall of the pipe string and the surface area of the inner wall of the wellbore.
 6. The method of claim 5 wherein the amount is a function of the determined pressure change and the empirical correction factor.
 7. The method of claim 1 wherein an empirical correction factor is used to adjust the wellbore fluid pressure to the corrected wellbore fluid pressure, the empirical correction factor being a function of the rate of movement of the pipe string, the surface area of the outer wall of the pipe string and the surface area of the inner wall of the wellbore.
 8. The method of claim 7 wherein the empirical correction factor is calibrated by measuring pressure proximate a bottom end portion of the pipe string.
 9. The method of claim 1 further comprising the steps of: operating a back pressure system to maintain the corrected wellbore fluid pressure in the annular space of the wellbore near a selected value during any rate of movement of the pipe string within the wellbore, the backpressure system being arranged and designed to apply a back pressure on the annular space of the wellbore.
 10. The method of claim 1 wherein the amount of adjusting corresponds to surge pressure indicative of pipe string movement into the wellbore.
 11. The method of claim 1 wherein the amount of adjusting corresponds to swab pressure indicative of pipe string movement out of the wellbore.
 12. The method of claim 1 wherein all of the steps are conducted in real time.
 13. A method for determining wellbore fluid pressure, corrected for movement of a pipe string within a wellbore, the method comprising the steps of: determining a rate of movement of a pipe string within a wellbore; determining an initial wellbore fluid pressure at a position within an annular space of the wellbore, the annular space being defined between an outer wall of the pipe string and an inner wall of the wellbore; determining a pressure change in the annular space of the wellbore resulting from movement of the pipe string; determining an empirical correction factor that is at least a function of the rate of movement of the pipe string, a surface area of the outer wall of the pipe string and a surface area of the inner wall of the wellbore; and adjusting the initial wellbore fluid pressure to a corrected wellbore fluid pressure by an amount that is a function of the determined pressure change and the empirical correction factor.
 14. The method of claim 13 wherein the step of determining a pressure change in the annular space of the wellbore resulting from movement of the pipe string is calculated using a flow rate of fluid flowing from the wellbore, the flow rate measured with a flow meter disposed in a fluid discharge conduit in fluid communication with the annular space of the wellbore.
 15. The method of claim 13 wherein the step of determining a pressure change in the annular space of the wellbore resulting from movement of the pipe string is a function of fluid displacement of the pipe string in the wellbore, the fluid displacement calculated using volumetric dimensions of the pipe string within the wellbore.
 16. The method of claim 13 wherein the empirical correction factor is calibrated by measuring pressure proximate a bottom end portion of the pipe string.
 17. The method of claim 13 wherein all of the steps are conducted in real time.
 18. A method for determining a pressure change in wellbore fluid pressure due to movement of a pipe string within a wellbore, the method comprising the steps of: determining a rate of movement of a pipe string within a wellbore; determining a pressure change in an annular space of the wellbore resulting from movement of the pipe string; the annular space being defined between an outer wall of the pipe string and an inner wall of the wellbore; determining an empirical correction factor that is at least a function of the rate of movement of the pipe string, a surface area of the outer wall of the pipe string and a surface area of the inner wall of the wellbore; and correcting the determined pressure change by an amount that is a function of the empirical correction factor.
 19. The method of claim 18 wherein the empirical correction factor is calibrated by measuring pressure proximate a bottom end portion of the pipe string.
 20. The method of claim 18 wherein all of the steps are conducted in real time. 